The invention relates to a new and distinct cultivar of Coleus plant that has been designated ‘UF15-20-6’. This cultivar originated from an open pollination between the female Coleus plant ‘UF14-14-8’ (unpatented) and an unknown male Coleus plant. This open pollination was conducted in Gainesville, Fla. from May through November of 2014. Asexual propagation of ‘UF15-20-6’ first occurred in Gainesville, Fla. in May of 2015 using meristem tip cuttings. That and all subsequent asexual propagations of ‘UF15-20-6’ have remained true-to-type and retained the distinctive features of this novel cultivar.